Calculus Examples

Find the Derivative - d/dx arcsin(1/( square root of x))
Step 1
Use to rewrite as .
Step 2
Differentiate using the chain rule, which states that is where and .
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Step 2.1
To apply the Chain Rule, set as .
Step 2.2
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate using the Power Rule.
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Step 3.1
Rewrite as .
Step 3.2
Multiply the exponents in .
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Step 3.2.1
Apply the power rule and multiply exponents, .
Step 3.2.2
Combine and .
Step 3.2.3
Move the negative in front of the fraction.
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Combine and .
Step 6
Combine the numerators over the common denominator.
Step 7
Simplify the numerator.
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Step 7.1
Multiply by .
Step 7.2
Subtract from .
Step 8
Move the negative in front of the fraction.
Step 9
Combine and .
Step 10
Multiply by .
Step 11
Simplify the expression.
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Step 11.1
Move to the left of .
Step 11.2
Move to the denominator using the negative exponent rule .
Step 12
Simplify.
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Step 12.1
Apply the product rule to .
Step 12.2
Combine terms.
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Step 12.2.1
One to any power is one.
Step 12.2.2
Multiply the exponents in .
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Step 12.2.2.1
Apply the power rule and multiply exponents, .
Step 12.2.2.2
Cancel the common factor of .
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Step 12.2.2.2.1
Cancel the common factor.
Step 12.2.2.2.2
Rewrite the expression.
Step 12.2.3
Simplify.
Step 12.3
Simplify the denominator.
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Step 12.3.1
Write as a fraction with a common denominator.
Step 12.3.2
Combine the numerators over the common denominator.
Step 12.3.3
Rewrite as .
Step 12.3.4
Multiply by .
Step 12.3.5
Combine and simplify the denominator.
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Step 12.3.5.1
Multiply by .
Step 12.3.5.2
Raise to the power of .
Step 12.3.5.3
Raise to the power of .
Step 12.3.5.4
Use the power rule to combine exponents.
Step 12.3.5.5
Add and .
Step 12.3.5.6
Rewrite as .
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Step 12.3.5.6.1
Use to rewrite as .
Step 12.3.5.6.2
Apply the power rule and multiply exponents, .
Step 12.3.5.6.3
Combine and .
Step 12.3.5.6.4
Cancel the common factor of .
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Step 12.3.5.6.4.1
Cancel the common factor.
Step 12.3.5.6.4.2
Rewrite the expression.
Step 12.3.5.6.5
Simplify.
Step 12.3.6
Combine using the product rule for radicals.
Step 12.3.7
Combine exponents.
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Step 12.3.7.1
Combine and .
Step 12.3.7.2
Combine and .
Step 12.3.8
Reduce the expression by cancelling the common factors.
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Step 12.3.8.1
Move to the numerator using the negative exponent rule .
Step 12.3.8.2
Multiply by by adding the exponents.
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Step 12.3.8.2.1
Move .
Step 12.3.8.2.2
Use the power rule to combine exponents.
Step 12.3.8.2.3
To write as a fraction with a common denominator, multiply by .
Step 12.3.8.2.4
Combine and .
Step 12.3.8.2.5
Combine the numerators over the common denominator.
Step 12.3.8.2.6
Simplify the numerator.
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Step 12.3.8.2.6.1
Multiply by .
Step 12.3.8.2.6.2
Add and .
Step 12.4
Multiply by .
Step 12.5
Combine and simplify the denominator.
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Step 12.5.1
Multiply by .
Step 12.5.2
Move .
Step 12.5.3
Raise to the power of .
Step 12.5.4
Raise to the power of .
Step 12.5.5
Use the power rule to combine exponents.
Step 12.5.6
Add and .
Step 12.5.7
Rewrite as .
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Step 12.5.7.1
Use to rewrite as .
Step 12.5.7.2
Apply the power rule and multiply exponents, .
Step 12.5.7.3
Combine and .
Step 12.5.7.4
Cancel the common factor of .
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Step 12.5.7.4.1
Cancel the common factor.
Step 12.5.7.4.2
Rewrite the expression.
Step 12.5.7.5
Simplify.
Step 12.6
Multiply by by adding the exponents.
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Step 12.6.1
Move .
Step 12.6.2
Multiply by .
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Step 12.6.2.1
Raise to the power of .
Step 12.6.2.2
Use the power rule to combine exponents.
Step 12.6.3
Write as a fraction with a common denominator.
Step 12.6.4
Combine the numerators over the common denominator.
Step 12.6.5
Add and .
Step 12.7
Reorder factors in .